Annex 3: Formal Specifications of Competitiveness Measures
A. DRC Ratios
The formal definition of the DRC199 is:
Figure 5: Formal Definition of Domestic Resource Cost Ratio
DRC = ∑(D*Pd)/(Wpi - ∑ajiWpj)
where i and j refer to internationally traded output and inputs respectively and Wp is their
world price; aji is the units of input j per unit of i. D is set of domestic factors of
production required to produce a unit of i and Pd is their economic or shadow price value.
In theory, all indirectly traded inputs into good(s) used to produce i should be included in
the denominator with a negative sign as part of ∑j.
Economic efficiency requires that DRC be less than the long-run value of foreign
exchange to the economy (the shadow exchange rate).
Benefits in this analysis are solely in terms of foreign exchange. However, in principle, it
is also possible to incorporate additional external effects either positive or negative.
Where these can be converted into an equivalent value in foreign currency (E), the DRC
becomes:
Figure 6: Calculation of Domestic Resource Cost Ratio Incorporating Foreign Exchange Equivalent
Values for External Effects
DRC = ∑(D*Pd)/(Wpi - ∑ajiWpj) + E
where E can be either positive or negative.
The analysis used in this report is compatible with project calculations as in the standard
literature, 200 where for a project producing internationally traded output and using
internationally traded and non-traded inputs and labor, economic net benefits in a single
year valued at domestic prices (EB) can be expressed as:
Figure 7: Calculation of Single-year Economic Net Benefits
EB = (To - Ti)*(SER) – (NTs + NTd + L)
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200
The classic statement of this approach is Bruno (1972).
UNIDO (1972), Little and Mirrlees (1974) and Squire and van der Tak (1975).
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where To and Ti are the border value of traded output and inputs, respectively, SER is the
shadow value of the exchange rate, NTs and NTd are non-traded inputs taken from the
supply margin and demand margin, respectively, and L is labor.
All values are in domestic currency, and SER is the shadow exchange rate. L should be
valued at the shadow wage, NTs at the economic cost of supply and NTd at willingness
to pay for the diverted inputs. In the standard DRC version shown in Figure , capital cost
is an annual charge, which should be decomposed into traded goods, non-traded goods
and labor.
Efficiency using the calculation in Figure implies EB > 1, which can be rearranged as an
alternative measure of efficiency as follows:
Figure 8: Calculation of Alternative Measure of Efficiency for Economic Net Benefits
(NTs + NTd + L)/(To - Ti)*(SER) < 1
This is the DRC ratio used in the analysis of this report.
A rigorous version of Figure would further decompose non-traded items in variable
supply (NTs) into traded goods and labor with the former traded inputs into non-traded
goods deducted from the denominator. 201 This report does not introduce these
complications and adopts the further simplifying assumptions:
1) Initially SER equals the current actual exchange rate (OER);
2) All non-traded inputs are expandable at the supply margin, so economic value is
determined by their cost of production not willingness to pay, so NTd = 0;
3) The shadow wage and the actual wage are equal; and
4) There are no externalities.
The economic supply cost for NTs is approximated by adjusting for first-round effects;
indirect taxes are deducted from NTs and traded inputs into the non-traded sectors are
included in the denominator under Ti. Thus this version of the DRC is:
Figure 9: Calculation of Domestic Resource Cost Adjusted for First-round Effects
DRC = (NTs + L)/(To – Ti)*OER
201
This is the reason why (ignoring non-traded goods in fixed supply) Little and Mirrlees (1974:363)
characterized the DRC approach as ‗the labor cost per unit of foreign exchange saving‘.
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This is an approximation but it is consistent with the commonly used simple efficiency
measure in operational economic appraisals. There EB is often calculated as shown in
Figure 2:
Figure 20: Commonly Used Simple Efficiency Measure of Economic Benefit
EB = (Ti - To)*(SER) – (NTs + L)
where labor may or may not be valued at a shadow wage, and domestic inputs are treated
as non-traded goods in variable supply whose value is determined by deducting taxes
from market prices. Subsequent calculations can test the results for alternative
assumptions about the value of foreign exchange.
The shadow exchange rate (SER) is the key parameter for testing efficiency or
inefficiency in the DRC approach. The shadow exchange rate is interpreted here as the
long-run value of foreign currency to an economy.202 The DRC analysis compares this
with the estimated cost in domestic resources per unit of foreign exchange to establish if
there is a net welfare benefit. Applied project analysis with the SER typically utilizes
tariff and subsidy data to estimate the difference between domestic and world prices in
the economy (as explained in the text), and then the shadow exchange rate ratio (or
premium on foreign exchange) becomes as shown in Figure 3:
Figure 31: Calculation of Shadow Exchange Rate Ratio
SER/OER = ∑μi(1 + ti - si) + ∑μj(1 – tj +sj)
where for import good i and export good j, μi and μj are share of good i and j,
respectively, in the value of additional foreign exchange made available by a project, t
and s refer to import or export taxes and subsidies, and the summation refers to all traded
goods affected.203
Theoretically the trade shares μi and μj are the value of additional importable and
exportable goods made available as a result of the change in the exchange rate created by
extra foreign exchange and will be determined by the price elasticities of demand for
different goods. Simple applications often assume elasticities are equal for each product.
202
In the cost benefit literature it is defined as the addition to welfare generated by the availability of one
extra unit of foreign exchange made available by the activity or project under consideration. Londero
(2003) Chapter 2 has an extensive discussion of the shadow exchange rate from a project perspective with
both a general equilibrium derivation and a discussion of simple operational formulae.
203
Figure 3 is equivalent to the classic definition of the shadow price of foreign exchange in Harberger
(1973).
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This analysis has the potentially serious limitation of ignoring long-term real exchange
rate adjustments. Where the current exchange rate of an economy does not reflect the
rate necessary for long-run internal and external balance, the long-run equilibrium real
exchange rate must be used to derive the SER for use in DRC analysis. 204 When an
underlying disequilibrium is introduced, the expression in Figure 3 must be modified to
become the calculation as shown in Figure:
Figure 12: Calculation of Shadow Exchange Rate Ratio in Conditions of Exchange Rate
Disequilibrium
SER/OER = (EER/OER)*(∑μi(1 + ti - si) + ∑μj(1 – tj +sj))
where EER is the long-run equilibrium real exchange rate.
This simplifies to:
Figure 43: Simplified Calculation of Shadow Exchange Rate in Conditions of Exchange Rate
Disequilibrium
SER = EER*(∑μi(1 + ti - si) + ∑μj(1 – tj +sj))
where Figure 4 defines the SER as the long-run equilibrium real exchange rate adjusted
for the net effect of tariffs and subsidies on trade that raises domestic prices above world
levels. The ratio of the EER to the OER can be interpreted as the future depreciation or
appreciation of the exchange rate necessary for long-run internal and external balance.
In recent years, the incidence of tariffs, taxes and subsidies on trade has declined
significantly for most economies. In practice, for the majority of countries, this report
suggests that the SER for use in the DRC analysis can be based on an estimate of the
long-run equilibrium real exchange rate, as in practice changes in EER relative to the
actual exchange rate are likely to dominate the net effect of trade taxes and subsidies.
This is not an easy parameter to estimate, and in practice it may have to be used as part of
sensitivity analysis testing the implications of different values on efficiency. However,
where average import tariffs remain high, there will be a need incorporate these in the full
expression for the SER.
There is a close similarity between the DRC indicator and the effective rate of protection.
Where there is no shadow pricing of domestic resources or foreign exchange (so SER =
OER) and non-traded inputs are treated as part of value added, the equivalence is that
value added at domestic prices equals domestic resource costs and value added at world
204
Edwards (1991) develops the concept of an equilibrium real exchange rate based on a set of underlying
fundamental factors affecting an economy; Chudik and Mongardini (2007) and Hobdari (2008) are recent
empirical applications of this approach in the African context.
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prices equals net foreign exchange. This means that the effective rate of protection
(ERP) is as noted in Figure :
Figure 14: Calculation of Effective Rate of Protection
ERP = (VAdp - VAwp)/VAwp or VAdp/VAwp - 1
where value added at world prices (VAwp) is equivalent to (To - Ti)*OER in Figure, and
value added at domestic prices (VAdp) is equivalent to (NTs + L) in Figure.
From the expression in Figure, DRC = (NTs + L)/(To - Ti)*OER, so:
Figure 15: Calculation of Domestic Resource Cost and Effective Rate of Protection Given Value
Added
DRC = VAdp/VAwp
ERP = DRC - 1.
This has the implication that efficient activities where DRC < 1 will have a negative ERP,
or in other words protection on output will be less than protection on inputs, so valueadded with protection is less than what it would be in a free trade situation.
When tariff rates are used to proxy the differences between world and domestic prices,
and there is no further shadow price adjustment to domestic resources, implicitly the
analysis is calculating effective rates of protection.
B. Trade Structure Indicators
The idea that the output and trade structure of poor countries matters for their economic
performance has a long history in development economics and is linked with discussions
of the importance of industrialization. Recent literature has formalized this approach by
stressing the need to upgrade the export structure of poor countries to higher levels of
technological content.
The starting point for analysis is the existing pattern of
specialization based on the Revealed Comparative Advantage (RCA) measure for product
i and country j, as shown in Figure .
Figure 16: Calculation of Revealed Comparative Advantage Measure for a Given Product and
Country
RCAij = (Xij/Xtj)/(Xit/Xwt)
where X is exports, w is the world and t is total.
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Thus RCAij is the share of i in the total exports of country j divided by the share of i in
total world exports. Thus a RCA > 1 implies the country is more specialized in a product
than is the world economy as whole, and the higher the RCA, the greater is the degree of
specialization. The argument is that different patterns of specialization have different
implications for growth, and that poor countries need to upgrade their export structure
into higher value, technologically more sophisticated products, where it is anticipated
demand prospects on the world market will be stronger.
The analysis was advanced by path-breaking work by Lall (2000) which created a
taxonomy of products based on a combination of earlier data on their R&D intensity (that
is R&D costs as a proportion of sales value) and personal knowledge of industrial
processes, which has been used widely to classify export structure. This work groups
exports into nine technology categories by the R&D intensity measure. The vast of
majority of manufactured exports from most of sub-Saharan Africa are in the low
technology, labor-intensive and natural resource-based categories, with little in the
medium and high technology categories. For example, for Ethiopia in 2009,
manufactured exports were dominated by leather and footwear (57%), food and
beverages (25%) and textiles (12%), which are either natural resource-based or simple
labor-intensive goods.
A limitation of this analysis is that it does not allow for a distinction between production
processes and products, since even relatively technologically advanced goods still can
have simple labor-intensive stages in their production. In response to this, Lall, Weiss
and Zhang (2006) attempted to differentiate between products at the disaggregate level
and to create an index (calculated at the 4-digit level) to capture their sophistication. This
was done for 766 individual product categories by taking a weighted average of the
incomes of all exporters of the good concerned with the weights given by their share in
total world trade in the good. Hence the calculation in Figure:
Figure 17: Calculation of Sophistication Index for a Good
SIi = ∑(Xik/Xiw)*Yk
where SIi is the sophistication index for good i, Xik is exports of i from country k, Xiw is
world exports of i, Yk is income per capita in country k and summation is for all k.
Lall, Weiss and Zhang (2006) use SI in various ways, including country ranking at the
aggregate level (where SI is aggregated over all products in total trade), for comparing
technology classifications and for establishing patterns within broad categories like
textiles and electronics. The rationale is that within individual product categories, the
average income of exporting countries can be a useful proxy for the technological depth
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of a product; hence an electrical good from Japan may be deemed to have higher
technology content than the same good from the Philippines. Similarly, within apparel,
products exported by rich countries – or processes undertaken by them – are taken to be
more skill, technology or marketing intensive and to yield higher profit margins and
wages than the more standardized goods exported by poorer countries.
Independently, Hausmann, Hwang and Rodrik (2007) applied the same approach, but
using a different weighting system. Here PROD represents the income level of a
particular good (calculated at the 6-digit level), but unlike the SI, the weights used are the
revealed comparative advantage of each country in the good concerned. Hence:
Figure 58: Calculation of Income Level for a Good
PRODi = ∑((Xik/Xtk)/(Xiw/Xtw))*Yk
where PRODi is the income level for good i, as before Xik is exports of i from country k,
Xiw is world exports of i, Yk is income per capita in country k and summation is for all k.
In addition, Xtk is the total exports of country k, and Xtw is total world exports.
The expression in Figure 5 can be rearranged as follows:
Figure 19: Alternative Calculation of Income Level for a Good
PRODi = ∑((Xik/Xiw)*(Xtw/Xtk))*Yk
The weights that result from the expression in brackets in Figure are then normalized to
sum to unity. The difference from the procedure in Figure is that now the share of
country k in world trade in product i is multiplied by the inverse of country k‘s share in
total world trade. This has the effect, which is intentional, of giving a higher weight to
goods exported from small countries. Hence, in this view, even if the US exports more
shirts than, say Bangladesh, if shirts are a product in which Bangladesh has specialized,
but the US has not, the US exports should be seen as a low productivity product.
Hausmann, Hwang and Rodrik (2007) apply their PROD indicator to total trade of
individual countries to calculate an overall measure akin to the sophistication index.
What they term the ‗productivity level of an economy‘s export basket‘ (EXPY) is a
weighted average of PROD for all commodities with the weights given by their share in a
country‘s trade. Their focus is on long-term trends, and they relate EXPY to growth
performance over time and contrast actual EXPY with that expected for an economy‘s
income level.
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African countries have the lowest EXPY score in their sample. For example, for 2001,
the values for Niger and Ethiopia are US$2,398 and US$2,715, respectively (in 2000 US
dollars), as compared with the highest score in the sample of US$24,552 for Luxembourg.
When they incorporate their productivity of exports measure in a growth analysis, they
find that, when controlling for a range of other factors, countries with a low productivity
export basket grow more slowly.
The policy implication of this analysis is that it is important to look to ways of raising the
technological sophistication and productivity levels of production, and exports even if in
the short-term it may appear to run counter to comparative advantage. In terms of the
DRC analysis, this can be interpreted as a distinction between a medium-run and a longrun DRC. However, there will be many new products to which a poor country
realistically cannot aspire to produce, so its DRC is unacceptably high. The difficulty of
moving into a new product is linked directly with the degree of specificity of the assets,
capabilities and operating environment (such as the physical assets, labor skills,
technological knowledge and infrastructure needs) associated with the products in which
a country currently is specialized. Where these attributes are either very general – i.e.,
relevant for the production of a wide range of goods – or production conditions are
similar in the new products, the transition to a new specialization may be relatively easy.
For any economy, there will be some ‗new goods,‘ in which the economy does not
currently specialize but which are relatively easy into which to move. These are ‗nearby‘
products where economic distance is low due to the similarity of the assets and
capabilities the products require relative to those needed by the economy‘s current pattern
of specialization.
The concept of economic distance is developed formally by Hausmann and Klinger
(2006) who calculate the probability that two countries both will have a comparative
advantage in different pairs of products. The higher the probability, the lower is the
distance between the two products. If products are grouped by broad classifications,
some are found to be peripheral in the sense that distance is low within the group but high
between the group and others. These peripheral groups typically are primary products,
but also include garments.
An important insight of the PROD and SI indicators are that they reveal that, even within
what are generally low productivity or unsophisticated groups (like textiles or clothing
for example), there will be some product lines with higher than average PROD or SI
scores, and it may be relatively easy for poor countries to move into production of higherscoring product lines. This shift into ‗nearby‘ products is a relatively easy way of raising
the overall EXPY score for a country and is something to be supported by policy. For
example, using 2006 US dollars, UNIDO (2011) shows that within the HS Code for
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clothing, the PROD score ranges from US$5,316 (HS 8464 under garments) to
US$11,066 (HS 8482 other apparel). Hence, there is scope for upgrading production in
similar product lines to those in which most poor economies are already operating.
Screening at the sub-sector level will not be able to distinguish these higher productivity
‗nearby‘ products, and for this, individual market studies will be needed.
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